Optimal control of customer admission to an open Jackson network

In this paper we consider the admission control problem of an open Jackson network. The external arriving customers are controlled by an admission control policy. Customer gets a reward for its service completion and pays a cost for its waiting time. The complete information of system state is not available for the controller. The admission control policy can observe only the number of total customers in the network. Therefore, the controller makes decision only at the epoch when the event of customer arrival happens. This is called the event-based control. Based on the special structure of system, we prove that the optimal control policy has a threshold form. That is, when the number of total customers is smaller than a threshold, all of the arriving customers are admitted; otherwise, all are rejected. We develop a very concise and iterative algorithm to find the optimal threshold. Simulation experiments are conducted to verify the main idea of this paper.